To determine what percentage of the dresses in the pie chart would be labeled "Blue," we need to follow these steps:
1. Calculate the total number of dresses:
We sum the counts of dresses in each category.
[tex]\[
\text{Total dresses} = 14 \, (\text{Red}) + 37 \, (\text{Black}) + 22 \, (\text{Blue}) + 56 \, (\text{White}) + 33 \, (\text{Other})
\][/tex]
Adding these values, we get:
[tex]\[
14 + 37 + 22 + 56 + 33 = 162
\][/tex]
2. Determine the proportion of blue dresses:
Next, we need to find out what fraction of the total dresses are blue. This can be done by dividing the count of blue dresses by the total number of dresses.
[tex]\[
\text{Proportion of blue dresses} = \frac{22 \, (\text{Blue})}{162 \, (\text{Total dresses})}
\][/tex]
3. Convert the proportion to a percentage:
To find the percentage, we multiply the proportional value by 100.
[tex]\[
\text{Percentage of blue dresses} = \left( \frac{22}{162} \right) \times 100
\][/tex]
4. Perform the calculation:
Dividing 22 by 162 gives approximately:
[tex]\[
\frac{22}{162} \approx 0.135802469
\][/tex]
Multiplying by 100 to convert this to a percentage:
[tex]\[
0.135802469 \times 100 \approx 13.580246913580247
\][/tex]
5. Round to the nearest percent:
To present this value in a more readable format, we round it to the nearest whole number.
[tex]\[
13.580246913580247 \approx 14
\][/tex]
Therefore, the percentage of the dresses that the sector labeled "Blue" would include in the pie chart is approximately [tex]\( 14\% \)[/tex].
